explain xkcd - User contributions [en]

Talk:2358: Gravitational Wave Pulsars

2020-09-13T02:29:18Z

Adam1729:

This one isn't very funny..
[[Special:Contributions/162.158.75.190|162.158.75.190]] 19:37, 11 September 2020 (UTC)
::It's not topical either. I sense filler. [[Special:Contributions/162.158.186.100|162.158.186.100]] 19:49, 11 September 2020 (UTC)
::::Perhaps not as topical as US Presidential Elections or COVID-19, but there have been at least two research papers on gravity wave phenomena in the past two weeks, I’ve been seeing YouTube vids about it pop up in my feed and various people tweeting about it. See the research paper, "GW190521: A Binary Black Hole Coalescence with a Total Mass of 150 Solar Masses," which was published in Physical Review Letters on September 2, 2020 and The research paper, "Properties and Astrophysical Implications of the 150 Solar Mass Binary Black Hole Merger GW190521," published in Astrophysical Journal Letters on September 2, 2020. [[Special:Contributions/108.162.219.58|108.162.219.58]] 05:13, 12 September 2020 (UTC)
::Unless there's a hidden joke that I don't get [[Special:Contributions/172.68.141.176|172.68.141.176]] 20:05, 11 September 2020 (UTC)
::There's a common joke that roughly goes "What is the secret to a good joke timing?" (said all at once) [[Special:Contributions/162.158.106.244|162.158.106.244]] 21:18, 11 September 2020 (UTC)

Context is here: https://arxiv.org/abs/2009.04496
::Related to this? [[https://en.wikipedia.org/wiki/GW190521 GW190521 Wiki]] [[User:OhFFS|OhFFS]] ([[User talk:OhFFS|talk]]) 21:13, 11 September 2020 (UTC)
::No, the gravitational waves have different periods than what LIGO/Virgo detects, and therefore the astrophysical sources are different. [[Special:Contributions/162.158.75.200|162.158.75.200]] 21:22, 11 September 2020 (UTC)

This is a reference to the (possibly apocryphal) Johnny Carson interview of a comedian (possibly Jerry Lewis, possibly Buddy Hackett):
* Comedian: Go ahead: ask me what is the secret of comedy.
* Carson: OK, what is the...
* Comedian: TIMING!
I've looked for the source, and all I can find are retellings of retellings (e.g. https://www.sleuthsayers.org/2013/08/the-immortal-timing-of-elmore-leonard.html ). -- [[User:Dtgriscom|Dtgriscom]] ([[User talk:Dtgriscom|talk]]) 02:35, 12 September 2020 (UTC)

I think the title text is referring to the saying I’m realty that the most important things to consider when buying a house are “location, location, location.” (https://www.realestateabc.com/insights/location.html)
[[Special:Contributions/108.162.238.5|108.162.238.5]] 03:34, 12 September 2020 (UTC)
:Which is good to know, but leaves some doubt over momentum, momentum and momentum. [[Special:Contributions/162.158.158.197|162.158.158.197]] 08:24, 12 September 2020 (UTC)

The use of curly braces around {location, location, location} might also be a joke.
"...using curly braces refers to the character vector that is stored within the string."
https://www.sciencedirect.com/topics/engineering/curly-brace
I don't understand enough about the topic to be sure. ---- JM
::The link points to a specific syntax for one programming language, namely MATLAB. Other languages use {...}, of course, but equally common is (...) or [...]. But importantly it is not a standard math/physics/astronomy notation. In a paper, unless otherwise specified, (x, y, z) is a triple of numbers making a vector whereas {x, y, z} is the set containing x, y, z and nothing else, which might therefore have 1, 2 or 3 elements. If there’s any joke here, it’s that {location, location, location} = {location}.

I've forgotten 110% of what I learned about math, but I thought {length, length, length} (or, equivalently, angle and magnitude) were equally important to a vector in 3-space. [[Special:Contributions/172.69.62.160|172.69.62.160]] 18:22, 12 September 2020 (UTC)

Talk:2358: Gravitational Wave Pulsars

2020-09-13T02:27:51Z

Adam1729:

This one isn't very funny..
[[Special:Contributions/162.158.75.190|162.158.75.190]] 19:37, 11 September 2020 (UTC)
::It's not topical either. I sense filler. [[Special:Contributions/162.158.186.100|162.158.186.100]] 19:49, 11 September 2020 (UTC)
::::Perhaps not as topical as US Presidential Elections or COVID-19, but there have been at least two research papers on gravity wave phenomena in the past two weeks, I’ve been seeing YouTube vids about it pop up in my feed and various people tweeting about it. See the research paper, "GW190521: A Binary Black Hole Coalescence with a Total Mass of 150 Solar Masses," which was published in Physical Review Letters on September 2, 2020 and The research paper, "Properties and Astrophysical Implications of the 150 Solar Mass Binary Black Hole Merger GW190521," published in Astrophysical Journal Letters on September 2, 2020. [[Special:Contributions/108.162.219.58|108.162.219.58]] 05:13, 12 September 2020 (UTC)
::Unless there's a hidden joke that I don't get [[Special:Contributions/172.68.141.176|172.68.141.176]] 20:05, 11 September 2020 (UTC)
::There's a common joke that roughly goes "What is the secret to a good joke timing?" (said all at once) [[Special:Contributions/162.158.106.244|162.158.106.244]] 21:18, 11 September 2020 (UTC)

Context is here: https://arxiv.org/abs/2009.04496
::Related to this? [[https://en.wikipedia.org/wiki/GW190521 GW190521 Wiki]] [[User:OhFFS|OhFFS]] ([[User talk:OhFFS|talk]]) 21:13, 11 September 2020 (UTC)
::No, the gravitational waves have different periods than what LIGO/Virgo detects, and therefore the astrophysical sources are different. [[Special:Contributions/162.158.75.200|162.158.75.200]] 21:22, 11 September 2020 (UTC)

This is a reference to the (possibly apocryphal) Johnny Carson interview of a comedian (possibly Jerry Lewis, possibly Buddy Hackett):
* Comedian: Go ahead: ask me what is the secret of comedy.
* Carson: OK, what is the...
* Comedian: TIMING!
I've looked for the source, and all I can find are retellings of retellings (e.g. https://www.sleuthsayers.org/2013/08/the-immortal-timing-of-elmore-leonard.html ). -- [[User:Dtgriscom|Dtgriscom]] ([[User talk:Dtgriscom|talk]]) 02:35, 12 September 2020 (UTC)

I think the title text is referring to the saying I’m realty that the most important things to consider when buying a house are “location, location, location.” (https://www.realestateabc.com/insights/location.html)
[[Special:Contributions/108.162.238.5|108.162.238.5]] 03:34, 12 September 2020 (UTC)
:Which is good to know, but leaves some doubt over momentum, momentum and momentum. [[Special:Contributions/162.158.158.197|162.158.158.197]] 08:24, 12 September 2020 (UTC)

The use of curly braces around {location, location, location} might also be a joke.
"...using curly braces refers to the character vector that is stored within the string."
https://www.sciencedirect.com/topics/engineering/curly-brace
I don't understand enough about the topic to be sure. ---- JM
::The link points to a specific syntax for one programming language, namely MATLAB. Other languages use {...}, of course, but equally common is (...) or [...]. But importantly it is not a standard math/physics/astronomy notation. In a paper, unless otherwise specified, (x, y, z) is a triple of numbers making a vector whereas {x, y, z} is the set containing x, y, z and nothing else, which might therefore have 1, 2 or 3 elements. If there’s any joke here, it’s that {location, location, location} = {location}, but I’m not convinced.

I've forgotten 110% of what I learned about math, but I thought {length, length, length} (or, equivalently, angle and magnitude) were equally important to a vector in 3-space. [[Special:Contributions/172.69.62.160|172.69.62.160]] 18:22, 12 September 2020 (UTC)

Talk:2358: Gravitational Wave Pulsars

2020-09-13T02:25:51Z

Adam1729:

This one isn't very funny..
[[Special:Contributions/162.158.75.190|162.158.75.190]] 19:37, 11 September 2020 (UTC)
::It's not topical either. I sense filler. [[Special:Contributions/162.158.186.100|162.158.186.100]] 19:49, 11 September 2020 (UTC)
::::Perhaps not as topical as US Presidential Elections or COVID-19, but there have been at least two research papers on gravity wave phenomena in the past two weeks, I’ve been seeing YouTube vids about it pop up in my feed and various people tweeting about it. See the research paper, "GW190521: A Binary Black Hole Coalescence with a Total Mass of 150 Solar Masses," which was published in Physical Review Letters on September 2, 2020 and The research paper, "Properties and Astrophysical Implications of the 150 Solar Mass Binary Black Hole Merger GW190521," published in Astrophysical Journal Letters on September 2, 2020. [[Special:Contributions/108.162.219.58|108.162.219.58]] 05:13, 12 September 2020 (UTC)
::Unless there's a hidden joke that I don't get [[Special:Contributions/172.68.141.176|172.68.141.176]] 20:05, 11 September 2020 (UTC)
::There's a common joke that roughly goes "What is the secret to a good joke timing?" (said all at once) [[Special:Contributions/162.158.106.244|162.158.106.244]] 21:18, 11 September 2020 (UTC)

Context is here: https://arxiv.org/abs/2009.04496
::Related to this? [[https://en.wikipedia.org/wiki/GW190521 GW190521 Wiki]] [[User:OhFFS|OhFFS]] ([[User talk:OhFFS|talk]]) 21:13, 11 September 2020 (UTC)
::No, the gravitational waves have different periods than what LIGO/Virgo detects, and therefore the astrophysical sources are different. [[Special:Contributions/162.158.75.200|162.158.75.200]] 21:22, 11 September 2020 (UTC)

This is a reference to the (possibly apocryphal) Johnny Carson interview of a comedian (possibly Jerry Lewis, possibly Buddy Hackett):
* Comedian: Go ahead: ask me what is the secret of comedy.
* Carson: OK, what is the...
* Comedian: TIMING!
I've looked for the source, and all I can find are retellings of retellings (e.g. https://www.sleuthsayers.org/2013/08/the-immortal-timing-of-elmore-leonard.html ). -- [[User:Dtgriscom|Dtgriscom]] ([[User talk:Dtgriscom|talk]]) 02:35, 12 September 2020 (UTC)

I think the title text is referring to the saying I’m realty that the most important things to consider when buying a house are “location, location, location.” (https://www.realestateabc.com/insights/location.html)
[[Special:Contributions/108.162.238.5|108.162.238.5]] 03:34, 12 September 2020 (UTC)
:Which is good to know, but leaves some doubt over momentum, momentum and momentum. [[Special:Contributions/162.158.158.197|162.158.158.197]] 08:24, 12 September 2020 (UTC)

The use of curly braces around {location, location, location} might also be a joke.
"...using curly braces refers to the character vector that is stored within the string."
https://www.sciencedirect.com/topics/engineering/curly-brace
I don't understand enough about the topic to be sure. ---- JM
::The link points to a specific syntax for one programming language, namely MATLAB. Other languages us {...} of course, but equally common is (...) or [...]. But importantly it is not a standard math/physics/astronomy notation. Unless otherwise specified, (x, y, z) is a triple of numbers making a vector whereas {x, y, z} is the set containing x, y, z and nothing else, which might therefore have 1, 2 or 3 elements. If there’s any joke here, it’s that {location, location, location} = {location}, but I’m not convinced.

I've forgotten 110% of what I learned about math, but I thought {length, length, length} (or, equivalently, angle and magnitude) were equally important to a vector in 3-space. [[Special:Contributions/172.69.62.160|172.69.62.160]] 18:22, 12 September 2020 (UTC)

Talk:2343: Mathematical Symbol Fight

2020-08-08T02:09:06Z

Adam1729:

Can I get aleph-null aleph-shaped throwing stars? [[User:LunarNapolean|LunarNapolean]] ([[User talk:LunarNapolean|talk]]) 20:18, 7 August 2020 (UTC)

Apologies to whoever added the "citation needed" that I stepped on. -- brad

That zeta looks conspicuously bad. I wonder if this comic will get a cleaned-up version uploaded. [[Special:Contributions/108.162.237.16|108.162.237.16]] 20:51, 7 August 2020 (UTC)

[[Megan]] usually has shoulder-length hair, so the person being attacked by Ponytail is probably not Megan... except in so far as all brunettes in this comic are called 'Megan'. [[User:LtPowers|LtPowers]] ([[User talk:LtPowers|talk]]) 20:53, 7 August 2020 (UTC)
:Is one of them [[Danish]]? And one of them Megan? [[Special:Contributions/172.69.33.121|172.69.33.121]] 22:49, 7 August 2020 (UTC)

I think Randall is underestimating the weapon utility of psi. There's a real-world martial arts [https://en.wikipedia.org/wiki/Sai_(weapon) weapon] that looks somewhat like it.[[Special:Contributions/172.69.68.197|172.69.68.197]] 22:04, 7 August 2020 (UTC)
:I think he’s also seriously underestimating the value of keeping your fingers attached to your hand. Swords have guards for a reason. I’d pick the contour integral over anything else there.

Considering the title text, a bass clef looks pretty formidable, close to a bat'leth. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 00:31, 8 August 2020 (UTC)
:Yes, but the treble clef is the one in the title text, and that’s nothing like a Klingon {{w|bat'leth}}. I removed the comment from the table. [[User:Adam1729|Adam1729]] ([[User talk:Adam1729|talk]]) 02:09, 8 August 2020 (UTC)

These “weapons” seem strangely appropriate for xkcd’s stick figures... -cpl

Talk:2343: Mathematical Symbol Fight

2020-08-08T02:05:56Z

Adam1729:

Can I get aleph-null aleph-shaped throwing stars? [[User:LunarNapolean|LunarNapolean]] ([[User talk:LunarNapolean|talk]]) 20:18, 7 August 2020 (UTC)

Apologies to whoever added the "citation needed" that I stepped on. -- brad

That zeta looks conspicuously bad. I wonder if this comic will get a cleaned-up version uploaded. [[Special:Contributions/108.162.237.16|108.162.237.16]] 20:51, 7 August 2020 (UTC)

[[Megan]] usually has shoulder-length hair, so the person being attacked by Ponytail is probably not Megan... except in so far as all brunettes in this comic are called 'Megan'. [[User:LtPowers|LtPowers]] ([[User talk:LtPowers|talk]]) 20:53, 7 August 2020 (UTC)
:Is one of them [[Danish]]? And one of them Megan? [[Special:Contributions/172.69.33.121|172.69.33.121]] 22:49, 7 August 2020 (UTC)

I think Randall is underestimating the weapon utility of psi. There's a real-world martial arts [https://en.wikipedia.org/wiki/Sai_(weapon) weapon] that looks somewhat like it.[[Special:Contributions/172.69.68.197|172.69.68.197]] 22:04, 7 August 2020 (UTC)
:I think he’s also seriously underestimating the value of keeping your fingers attached to your hand. Swords have guards for a reason. I’d pick the contour integral over anything else there.

Considering the title text, a bass clef looks pretty formidable, close to a bat'leth. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 00:31, 8 August 2020 (UTC)
:Yes, but the treble clef is the one in the title text, and that’s nothing like a Klingon {{w|bat'leth}}. I removed the comment from the table.

These “weapons” seem strangely appropriate for xkcd’s stick figures... -cpl

2343: Mathematical Symbol Fight

2020-08-08T02:03:28Z

Adam1729: Treble clef nothing like a Klingon w|bat'leth

{{comic
| number = 2343
| date = August 7, 2020
| title = Mathematical Symbol Fight
| image = mathematical_symbol_fight.png
| titletext = Oh no, a musician just burst in through the door confidently twirling a treble clef.
}}

==Explanation==
{{incomplete|Created by a SQUARE ROOT SCYTHE. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

This panel imagines which {{w|List of mathematical symbols|mathematical symbols}} would be good in a fight if they were made corporeal in two (or three) dimensions. Generally, objects with longer reach and pointier ends wind up on the "more dangerous" side of the scale, and symbols with less reach and more curves tend towards the left side.

The comic invokes [[wikipedia:surreal humour|surreal humour]] by suggesting that mathematical symbols could be handled as physical objects in the real world. Another component of the humor is the implication that it is useful to prepare to use mathematical symbols in a fight, even though mathematicians, who use mathematical symbols, usually do not conduct their debates violently (though some stories suggest that {{w|Hippasus}} was killed by his fellow Pythagoreans for his proof that irrational numbers exist), and even if they did, they wouldn't use large reproductions of their symbols as weapons.{{Citation needed}}

A straight line is farthest to the "more dangerous" side, which could possibly be a reference to the dangers posed by lines in "Flatland", because their infinitely-sharp endpoints could be difficult to see (particularly their rear end, which does not contain a gleaming eye as their front end does) and would fatally pierce whoever they chose to stab. However, taking a more literal view of the drawings, the straight line does not appear to be any thicker or thinner, or pointer, than any of the other lines.

The title text refers to a {{w|clef}}, which is not a mathematical symbol but rather a {{w|List of musical symbols|musical symbol}}. The note of concern in the text suggests musical symbols may be viewed in such fights as exotic or especially dangerous.

{| class="wikitable"
! Symbol
! Meaning
! Notes on using in a fight
|-
|ℝ
|The set of [[wikipedia:real number|real number]]s
|Megan seems to be struggling with a giant version of this symbol.
|-
|∅
|[[wikipedia:Empty set|Empty set]]
|This symbol is not very sharp, and [[White Hat]] is unable to use it in combat. It would not work as a good shield due to the hole in the symbol, but it possibly could be thrown.
|-
|>
|Greater than
|-
|α
|[[wikipedia:Alpha_(disambiguation)#Mathematics_and_statistics|Alpha]]
|-
|π
|[[wikipedia:Pi_(disambiguation)#Mathematics|pi]]
|-
| +
|[[wikipedia:Plus_and_minus_signs#Plus_sign|Plus]]
|Maybe thrown like a shuriken?
|-
|Ψ
|[[wikipedia:Psi#Mathematics|Psi]]
|It could be used as a slightly-less-functional trident or pitchfork, with a shorter handle. More particularly, it resembles a sai (which, funnily enough, is how "Psi" is pronounced).
|-
|~
|[[wikipedia:Tilde#Mathematics|tilde]], meaning "approximately", equivalent, or several transforms of a function
|A potentially dangerous throwing weapon.
|-
|⇒
|[[wikipedia:Material_conditional|Material consequence]] or [[wikipedia:Logical_consequence|Logical consequence]], meaning "implies"
|-
|⋅
|multiplication sign
|-
|Γ
|uppercase Greek letter gamma
|-
|√
|{{w|square root}} sign
|Black Hat has chosen this symbol and is using it like a polearm, something like a {{w|shepherd's crook}}.
|-
|∮
|contour integral
|-
|∫
|integral
|-
|⇀
|vector denotation
|A single-barbed spear.
|-
|θ
|[[wikipedia:Theta_function_(disambiguation)|Theta]]
|-
|∞
|infinity
|-
|∪
|union (set theory)
|-
|∈
|member of (set theory)
|Cueball is holding this. It could be used as a significantly-less-functional trident or pitchfork, if only it wasn't missing a handle like Psi. Maybe better for throwing.
|-
|∀
|"for all"
|-
|∂
|[[wikipedia:Partial derivative|partial derivative]] or [[wikipedia:Boundary_(topology)|boundary operator]]
|-
|≠
|not equal sign
|-
|#
|[[wikipedia:Cardinality|Cardinality]], [[wikipedia:Connected_sum|connected sum]] (knot theory), or [[wikipedia:Primorial|primorial]].
|Blondie uses this symbol.
|-
|-
|Δ
|[[wikipedia:Delta_(letter)|Delta]]
|-
|ζ
|Zeta
|-
|ℵ
|[[wikipedia:Aleph_number|Aleph number]]
|-
|𝜌
|italic rho
|Perhaps could be wielded as a club
|-
|→
|Implies; X→Y means that if X is true, then Y is also true
|Looks like a spear
|-
|⊥
|up tack or falsum, indicating a false proposition in logic or the bottom element in a partial order
|Held like an axe, the top of the T could be arced towards an opponent.
Held like a wishbone, two hands could be used to try to drive the point into an opponent.
|-
|⎯⎯
|Fraction bar (division) or overline (complex conjugate or mean).
|Held on one end, this could be used to stab the point, or hit with the edge
|-
|-
|𝄞
|Treble clef
|Could potentially be 'twirled' like a {{w|quarterstaff}}, {{w|bō}}, or other {{w|stick-fighting}} weapon
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
[Heading]

Mathematical Symbols

[Subheading]

by how useful they would be in a fight

more useful

⟶

ℝ ∅ > α π + Ψ ~ ⇒ ⋅ Γ √ ∮ ∫ ⇀
θ ∞ ∪ ∈ ∀ ∂ ≠ # Δ ζ ℵ 𝜌 → ⊥ ⎯

[Below the (number?) line, eight characters fight each other, using some of the symbols mentioned above as weapons.]

[The characters hold more "useful" weapons from left to right, correlating with the chart.]

[Megan is awkwardly handling a giant "ℝ".]

[White Hat is holding an "∅" with both hands, as a shield.]

[Cueball is holding an "∈" in both hands, with its "tines" pointed towards Blondie, who is swatting at him with a "#".]

[Ponytail is leaping at Danish, swinging a "ρ" like an axe, while Danish is leaning back and thrusting a "→" back at her.]

[Black Hat is swinging a long "√" like a polearm at Hairy, who is holding a long "⎯" defensively.]

-
List of symbols from left to right (by rightmost edge):

ℝ θ ∅ ∞ > ∪ α ∈ ∀ π ∂ + ≠ Ψ # ~ △ ζ ⇒ ⋅ ℵ Γ 𝜌 √ → ∮ ∫ ⊥ ⇀ ⎯

Note: Where two symbols had similar right-most edges, the overlay grid on an ASUS pro-art display was used to decide which one went further right.

{{comic discussion}}
[[Category:Math]]
[[Category:Music]]
[[Category:Charts]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Danish]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Blondie]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Black Hat]]
[[Category:Comics featuring Hairy]]

2322: ISO Paper Size Golden Spiral

2020-06-21T19:19:32Z

Adam1729: Not quite a spiral

{{comic
| number = 2322
| date = June 19, 2020
| title = ISO Paper Size Golden Spiral
| image = iso_paper_size_golden_spiral.png
| titletext = The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 11/8.5 = pi/4.
}}

==Explanation==
{{incomplete|Created by a GRAPHICS DESIGNER. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

This comic strip is about how to annoy graphics designers and mathematicians, much like [[590: Papyrus]] and [[1015: Kerning]].

An easy way to annoy many mathematicians is to make fanciful claims about the {{w|Golden Ratio}}. It's been claimed, with varying levels of credibility, to be detectable in many natural and humanmade situations, often with the dubious subjective claim that using the ratio in some particular way makes an image more "beautiful". The {{w|Golden Spiral}} is a spiral whose growth factor is this ratio; a common (though slightly geometrically inaccurate) way to illustrate the spiral is to draw curves through a set of squares whose side lengths shrink according to the Golden Ratio. The result looks rather like Randall's drawing here.

However, Randall hasn't used the Golden Ratio at all; he's just drawn a spiral (''not'' the Golden Spiral) through a common diagram showing the {{w|Paper_size#A_series|A Series}} of standard paper sizes, but in horizontal instead of portrait (this diagram is commonly drawn in portrait). These papers aren't squares at all, but rectangles whose side lengths shrink by a factor of the square root of 2. Additionally, the paper sizes shrink by a factor of one half instead of 2**-0.5, so the paper sizes should all be either even or odd. By mistaking the A Series for something connected with the Golden Ratio, ''and'' perpetuating the tradition of making dubious claims about the Golden Ratio, Randall has successfully annoyed both graphics designers and mathematicians.

===Title text===

The title text is a similarly themed joke, based partly on the fact that the US uses customary units while much of the rest of the world uses SI units. The 11/8.5 ratio is the length/width ratio of {{w|Letter (paper size)|US Letter}} paper, which is 11 inches by 8.5 inches (another common size in the United States is US Legal, which is 14" by 8.5"). The value of pi/4 radians is indeed equal to 45 degrees, although Randall takes the cosine in one case and uses the raw angle in the other case in order to get a close coincidence of values. The width/length ratio of A Series paper ({{w|ISO 216}}) is exactly cos(45°), which is 1/sqrt(2). As for US Letter paper, 11/8.5 is not in fact close to pi/4, but it’s possible that Randall meant to write 8.5/11 instead of 11/8.5. To 4 decimal places, 8.5/11 = 0.7727 and pi/4 = 0.7854.

In reality, the usage of radians vs. degrees is not a geographic or political decision, but generally is delineated by profession. Most engineering and science fields measure angles in degrees or fractions of degrees (arcseconds, or even milliarcseconds in fields like astronomy), while mathematicians and physicists generally use radians. Civil engineers may refer to the slope of a road by its {{w|Grade (slope)|grade}}, which is commonly expressed in terms of the tangent of the angle to the horizontal (either as a percentage or a ratio); for angles up to ~10 degrees, this is close to the value of the angle in radians.

==Supplementary maths==
The difference between the "real" Golden Spiral squares and Randall's version is approximately either .2038 (for sqrt(2)-1.6180etc) or .08907 ((1/sqrt(2))-1.6180etc), depending on which way you're counting. Either way, the difference would be very noticeable.)

The spiral shown is approximately a logarithmic spiral with a growth factor of sqrt(2), although it has been edited slightly to make it fit neatly inside the rectangles.
If the center of the spiral is at the origin, it may be graphed with r = C*2^(θ/π), for any positive constant C.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Caption inside panel:]
:The golden ratio is everywhere!

:[Picture of the ISO standard paper sizes (i.e. A1, A2, etc.) placed so that they fit together perfectly, overlaid with a spiral resembling that of the golden ratio]

:[Caption below panel:] 
:How to annoy both graphic designers and mathematicians

{{comic discussion}}
[[Category:Math]]
[[Category:Comics with color]]

2322: ISO Paper Size Golden Spiral

2020-06-19T18:38:38Z

Adam1729: C positive

2322: ISO Paper Size Golden Spiral

2020-06-19T18:36:31Z

Adam1729: Letter, not legal

2322: ISO Paper Size Golden Spiral

2020-06-19T18:33:07Z

Adam1729: Corrected error root 2 versus 2

2322: ISO Paper Size Golden Spiral

2020-06-19T18:31:32Z

Adam1729: Explain ISO 216

2322: ISO Paper Size Golden Spiral

2020-06-19T18:24:48Z

Adam1729: correct ratio for A series scaling

2322: ISO Paper Size Golden Spiral

2020-06-19T18:22:35Z

Adam1729: Mouse-over text explanation

2034: Equations

2018-11-06T03:56:46Z

Adam1729: e^-\infty is an infinitesimal in non-standard analysis

{{comic
| number = 2034
| date = August 17, 2018
| title = Equations
| image = equations.png
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
}}
==Explanation==
{{incomplete|TODO: some simplified explanations. Do NOT delete this tag too soon.}}

This comic gives a set of equations supposedly from different areas of science in mathematics, physics, and chemistry. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. To someone who knows even a little about the topic, they are clearly very wrong and only seem even worse the more you look at them. In many disciplines, the mathematical description of a large area is summed up in a small number of equations, such as Maxwell's equations for electromagnetism. In similar fashion, the equations here purport to encompass the whole of their given field.

===Simplified Explanations===

;All kinematics equations
Kinematics is the study of the motion of objects. More specifically, it describes how the location, velocity, and acceleration of an object vary over time. The equation shown contains two of these standard kinematic variables, velocity ''v'' and time ''t'', in addition to several quantities (''E'', ''K0'', and ''ρ'') that are completely unrelated to kinematics.

;All number theory equations
Number theory is a branch of mathematics concerned primarily with the study of integers. However, the equation shown contains the non-integer Euler's constant ''e'' (approximately 2.718). It also uses the Greek letter π as an integer-valued variable, even though the symbol π is used in mathematics almost exclusively to denote the well-known ''non''-integer circle constant (approximately 3.14159). Even with π treated as a variable here, one of its uses in the equation is still unusual, to say the least. <math>\pi-\infty</math> is <math>-\infty</math>, so <math>e^{\pi-\infty}</math> is 0, making the <math>\pi</math> unnecessary.

;All chemistry equations
Randall implies that all chemistry is just combustion of chemicals, demonstrated with an incorrect form of a common example chemistry equation of burning Methane and Oxygen (with added heat), to form water and carbon dioxide. However, in this form "HEAT" is an actual molecule, rather than simply indicating the presence of heat to start the reaction. Thus the equation is modified to incorporate the fictional "HEAT" into the reaction. While the H in "HEAT" is the chemical symbol of the element hydrogen, none of the letters E, A, or T are symbols of any actual elements. Also, to account for the second hydrogen in "H(2)EAT" on the products side, the oxygen gas on the reactants side has been altered to be hydroxide, a strong base that would not facilitate traditional combustion.

TODO: other simplified explanations.

===Technical Explanations===
;All kinematics equations
:<math>E = K_0t + \frac{1}{2}\rho vt^2</math>
{{w|Kinematics}} describes the motion of objects without considering mass or forces. The latter is described by {{w|Kinetics (physics)|kinetics}}. The two fields get frequently confused due to the similarity of words.

This equation here literally states: "Energy equals a constant <math>K_0</math> multiplied by time, plus half of density multiplied by speed multiplied by time squared".

The first term here is hard to interpret: it could be correct if <math>K_0</math> is a constant power applied to the system, but this symbol would more normally be used to denote an initial energy, in which case multiplying by <math>t</math> would be wrong. Alternatively, the term is similar to <math>k_B T</math> (sometimes written as ''kT''), a term that often appears in {{w|Statistical_mechanics|statistical mechanics}} equations, where ''kB'' (or ''k'') is {{w|Boltzmann_constant|the Boltzmann constant}}, and ''T'' is the {{w|Thermodynamic_temperature|absolute temperature}}. In this latter case, the term would have units of energy, consistent with the left side of the equation.

The second term looks similar to the kinetic energy term <math> \frac{1}{2}\rho v^2 </math> in [http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html the Bernoulli equation] for fluids. (More properly, this is the kinetic energy ''density'' in the fluid).

The whole equation appears to be a play on the kinematics formula: <math>s = v_0t + \frac{1}{2}\ at^2</math>, where distance travelled (''s'') by a constantly accelerating object is determined by initial velocity (''v0''), time (''t''), and acceleration (''a'')

Kinematics is often one of the first topics covered in an introductory physics course, both at the high school and freshman college levels. As such, mixing in material from more advanced topics like statistical mechanics and the Bernoulli equation, even if done correctly, would be very confusing for a typical student learning kinematics.

;All number theory equations
:<math>K_n = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
{{w|Number theory}} is a branch of mathematics primarily studying the properties of integers.

Said in English, the equation can be read: "The ''n''th K-number is equal to the sum for all ''i'' from 0 to infinity of the sum for all π from 0 to infinity of ''n'' minus π, multiplied by ''i'' plus ''e'' raised to the power of π minus infinity." (''i'' here is an iteration variable, not the imaginary number constant; ''e'' is Euler's number, approximately 2.718). A twofold misconception can be seen here. The first is the use of π as a variable instead of the circle constant (3.14...). This might be a jab at how in number theory letters and numbers are used interchangeably, but where some letters are suddenly fixed constants.

Further confusion comes from the use of unusual mathematical models. While the term <math>e^{\pi-\infty}</math> is 0 when considered in standard ("high school") mathematics, it can be taken to be an infinitesimal in {{w|non-standard analysis}}, a concept unfamiliar to most non-mathematicians and uncommon in number theory. Naively, this would signify that (with the use of π as a variable) the exponent would range from negative infinity to zero. In fact, assuming ''e'' really does mean Euler's constant (or at least a real number strictly greater than 1) the term would be zero for every π < ∞. Ultimately, the sum diverges for every ''n''.

The close proximity of the letters i, e and π also evokes {{w|Euler's identity}} <math>e^{i\pi}+1=0</math> (also written <math>e^{i\pi}=-1</math>), without actually using it, especially since both π and i are used as variables here.

;All fluid dynamics equations
:<math>\frac{\partial}{\partial t}\nabla\cdot \rho = \frac{8}{23}
\int\!\!\!\!\!\!\!\!\!\;\;\bigcirc\!\!\!\!\!\!\!\!\!\;\;\int
\rho\,ds\,dt\cdot \rho\frac{\partial}{\partial\nabla}
</math>
{{w|Fluid dynamics}} describes the movement of non-solid material. In particular for gases, the density <math>\rho</math> is often the most interesting quantity (for liquids, this is often just constant). A unique feature of fluid-dynamic equations is the presence of {{w|Advection|advection terms}}, which take the form of often strange-looking spatial derivatives. This equation turns this up to a new level by differentiating with respect to a differential operator <math>\nabla</math>, which does not make any sense at all. Also it has a contour integral which seems reminiscent to a closed-circle process like in a piston engine, but this does not really fit in the context (differential description of a gas), and it has a pair of {{w|Magic number (programming)|unexplained numbers}} <math>8</math> and <math>23</math>, probably alluding to the {{w|Heat capacity ratio|specific heat ratio}} which is often written out as the fraction <math>\tfrac{7}{5}</math>, whereas most other physics equations [[899: Number Line|avoid including any plain numbers higher than 4]].

The title text stating that the electromagnetism equation is the same as the fluid dynamics equation, but with the arbitrary 8 and 23 replaced with the permittivity and permeability of free space is likely because electromagnetism equations often have relations to fluid dynamics, and because those two constants appear in the vast majority of electromagnetism equations.

;All quantum mechanics equations
:<math>|\psi_{x,y}\rangle = A(\psi) A(|x\rangle \otimes |y\rangle)</math>
{{w|Quantum mechanics}} is a fundamental theory in physics which describes nature at scales of atoms and below. It typically uses the {{w|Bra–ket notation|bra–ket notation}} in its formulae.

This equation takes a state psi in the dimensions of x and y and equates it to an operator A performed on psi multiplied by the same operator performed on the tensor product of x and y. Since the state psi is already the tensor product of the states x and y, this is equivalent to performing the same unknown operator twice on psi, and unless this operator is the identity or is its own inverse such as a bit-flip or Hermitian operator, this equation is therefore incorrect.

;All chemistry equations
:<math>\mathrm{CH}_4 + \mathrm{OH} + \mathrm{HEAT} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CH}_2 + \mathrm{H}_2 \mathrm{EAT}</math>
A {{w|Chemical equation|chemical equation}} represents a chemical reaction as a formula, with the reactant entities on the left-hand side, and the product entities on the right-hand side. The number of each element on the left side must match those on the right side. The energy produced or absorbed in this process is not included in that formula.

This is a modification of the combustion of methane. The correct form is often taught and a good example problem but obviously there are more chemistry problems.<math>\mathrm{HEAT}</math> is normally shorthand for {{w|activation energy}}, but in Randall's version it's jokingly used as a chemical ingredient and becomes <math>\mathrm{H}_2\mathrm{EAT}</math>, taking the hydrogen atom freed by the combustion equation shown. The proper methane combustion equation would be: <math>\mathrm{CH}_4 + 2 \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2</math>

While <math>\mathrm{OH}</math> often appears in chemical equations in the form of a negatively charged hydroxide group (<math>\mathrm{OH}^-</math>), the left side of the equation involves a bare <math>\mathrm{OH}</math>, possibly the highly unstable hydroxyl radical (although this would typically be written with a leading dot, e.g. <math>\bullet\mathrm{OH}</math>). Similarly, the right side contains an unstable methylene radical which would generally only appear as an intermediate rather than a product.

;All quantum gravity equations
:<math>\mathrm{SU}(2)\mathrm{U}(1) \times \mathrm{SU}(\mathrm{U}(2))</math>
This is more similar to expressions which appear in {{w|Grand_Unified_Theory|Grand Unified Theory}} (GUT) than general quantum gravity. Unlike some of the other equations, this one has no interpretation which could make it mathematically correct. This is similar to the notations used to describe the symmetry group of a particular phenomena in terms of mathematical {{w|Lie_Group|Lie Groups}}. A real example would be the Standard Model of particle physics which has symmetry according to <math>\rm{SU(3)\times SU(2) \times U(1)}</math>. Here, <math>\rm{SU}</math> and <math>\rm{U}</math> denote the special unitary and unitary groups respectively with the numbers indicating the dimension of the group. Loosely, the three terms correspond to the symmetries of the strong force, weak force and electromagnetism although the exact correspondence is muddied by symmetry breaking and the Higgs mechanism.

Of course, an expression missing an "=" sign, is difficult to interpret as an "equation", because equations normally express an "equality" of some kind. Nobody knows whether Randal refers to a horse, zebra, donkey or other equine here.

Randall's version clearly involves some similar groups although without the <math>\times</math> symbol it is hard to work out what might be happening. A term like <math>\rm{SU(U(2))}</math> has no current interpretation in mathematics, if anyone thinks otherwise and possibly has a solution to the quantum gravity problem they should probably get in touch with someone about that.

;All gauge theory equations
:[[File:All gauge theory equations.png]]
In physics, a {{w|Gauge theory|gauge theory}} is a type of field theory which is invariant to local transformations. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom.

This equation looks broadly similar to the sorts of things which appear in gauge theory such as the equations which define {{w|Yang–Mills_theory#Quantization|Yang-Mills Theory}}. By the time physics has got this far in, people have normally run out of regular symbols making a lot of the equations look very daunting. The actual equations in this field rarely go far beyond the Greek alphabet though and no-one has yet to try putting hats on brackets. The appearance of many sub- and superscripts is normal (this links to the group theory origins of these equations) and for the layperson it can be impossible to determine which additions are labels on the symbols and which are indices for an {{w|Einstein_notation|Einstein Sum}}.

The left-hand side <math>S_g</math> is the symbol for some {{w|Action_(physics)|action}}, in Yang-Mills theory this is actually used for a so-called "ghost action". On the right-hand side we have a large number of terms, most of which are hard to interpret without knowing Randall's thought processes (this is why real research papers should all label their equations thoroughly). The <math>\frac{1}{2\bar{\varepsilon}}</math> looks like a constant of proportionality which often appears in gauge theories. The factor of <math>i = \sqrt{-1}</math> is not unusual as many of these equations use complex numbers. The <math>\eth</math> symbol looks similar to a <math>\partial</math> partial derivative symbol especially as the {{w|Dirac_equation#Covariant_form_and_relativistic_invariance|Dirac Equation}} uses a slashed version as a convenient shorthand.

The rest of the equation cannot be mathematically correct as the choice of indices used does not match that on the left-hand side (which has none). In particle physics subscripts (or superscripts) of greek letters (usually <math>\mu</math> or <math>\nu</math>) indicate terms which transform nicely under Lorentz transformations (special relativity). Roman indices from the beginning of the alphabet relate to various gauge transformation propetries, the triple index seen on <math>p^{abc}_v</math> would likely come from some <math>\rm{SU(3)}</math> transformation (related to the strong nuclear force). Since <math>S_g</math> has none of these (and is thus a scalar which remains constant under these operations), we would need the right-hand side to behave in the same way. Most of the indices which appear are unpaired and so will not result in a scalar making the equation very wrong. For those not familiar with this type of equation, this is similar to the mistake of messing up units, for instance setting a distance equal to a mass.

;All cosmology equations
:<math>H(t) + \Omega + G \cdot \Lambda \, \dots \begin{cases} \dots > 0 & \text{(Hubble model)} \\ \dots = 0 & \text{(Flat sphere model)} \\ \dots < 0 & \text{(Bright dark matter model)} \end{cases}
</math>
This is a parody of equations defining the {{w|Hubble's_law#Derivation_of_the_Hubble_parameter|Hubble Parameter}} <math>H(t)</math> although it looks like Randall has become bored and not bothered to finish his equation. Such equations usually have several <math>\Omega</math> terms representing the contributions of different substances to the energy-density of the Universe (matter, radiation, dark energy etc.). In this context <math>G</math> could be Newton's constant and <math>\Lambda</math> is the cosmological constant (energy density of empty space) although seeing them appear multiplied and on the same footing as <math>H</math> is unusual (the dot is entirely unnecessary). Choosing to make <math>H</math> a function of time <math>t</math> and not of redshift <math>z</math> is also unusual.

The second section looks like the inequalities used to show how the equation varies with the shape of the Universe, based on the value of the curvature parameter <math>\Omega_k</math>. A value of 0 indicates a flat Universe (this is more or less what we observe) while a positive /negative value indicates an open /closed curved Universe. Randall's choice of labels further makes fun of the field as both a flat sphere and bright dark matter are oxymoronic terms which would involve some rather strange model universes.

;All truly deep physics equations
:[[File:All truly deep physics equations.png]]
<math>\hat H</math> is the Hamiltonian operator, which when applied to a system returns the total energy. In this context, U would usually be the potential energy. However, there is also a subscript 0 and a diacritic marking indicating some other variable. Much of physics is based on Lagrangian and Hamiltonian mechanics. The Lagrangian is defined as <math>\hat L = \hat K - \hat U </math> with K being the kinetic energy and U the potential. Hamiltonian mechanics uses the equation <math>\hat H = \hat K + \hat U </math>. The Hamiltonian must be conserved so taking the time derivative and setting it equal to zero is a powerful tool. The "principle of least action" allows most modern physics to be derived by setting the time derivative of the Lagrangian to zero.

==Transcript==
:[Nine equations are listed, three in the top row and two in each of the next three rows. Below each equation there are labels:]

:E = K0t + 1/2 ρvt2
:All kinematics equations

:Kn = ∑i=0∞∑π=0∞(n-π)(i-eπ-∞)
:All number theory equations

:∂/∂t ∇ ⋅ ρ = 8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
:All fluid dynamics equations

:|ψx,y〉 = A(ψ) A(|x〉⊗ |y〉)
:All quantum mechanics equations

:CH4 + OH + HEAT → H2O + CH2 + H2EAT
:All chemistry equations

:SU(2)U(1) × SU(U(2))
:All quantum gravity equations

:Sg = (-1)/(2ε̄) i ð (̂ ξ0 +̊ pε ρvabc η0 )̂ f̵a0 λ(ʒ̆) ψ(0a)
:All gauge theory equations

:[There is a brace linking the three cases together.]
:H(t) + Ω + G⋅Λ ...
:... > 0 (Hubble model)
:... = 0 (Flat sphere model)
:... < 0 (Bright dark matter model)
:All cosmology equations

:Ĥ - u̧0 = 0
:All truly deep physics equations

{{comic discussion}}

[[Category:Science]]
[[Category:Physics]]
[[Category:Math]]
[[Category:Chemistry]]
[[Category:Astronomy]]

2034: Equations

2018-11-06T03:51:44Z

Adam1729: /* Simplified Explanations */

{{comic
| number = 2034
| date = August 17, 2018
| title = Equations
| image = equations.png
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
}}
==Explanation==
{{incomplete|TODO: some simplified explanations. Do NOT delete this tag too soon.}}

This comic gives a set of equations supposedly from different areas of science in mathematics, physics, and chemistry. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. To someone who knows even a little about the topic, they are clearly very wrong and only seem even worse the more you look at them. In many disciplines, the mathematical description of a large area is summed up in a small number of equations, such as Maxwell's equations for electromagnetism. In similar fashion, the equations here purport to encompass the whole of their given field.

===Simplified Explanations===

;All kinematics equations
Kinematics is the study of the motion of objects. More specifically, it describes how the location, velocity, and acceleration of an object vary over time. The equation shown contains two of these standard kinematic variables, velocity ''v'' and time ''t'', in addition to several quantities (''E'', ''K0'', and ''ρ'') that are completely unrelated to kinematics.

;All number theory equations
Number theory is a branch of mathematics concerned primarily with the study of integers. However, the equation shown contains the non-integer Euler's constant ''e'' (approximately 2.718). It also uses the Greek letter π as an integer-valued variable, even though the symbol π is used in mathematics almost exclusively to denote the well-known ''non''-integer circle constant (approximately 3.14159). Even with π treated as a variable here, one of its uses in the equation is still unusual, to say the least. <math>\pi-\infty</math> is <math>-\infty</math>, so <math>e^{\pi-\infty}</math> is 0, making the <math>\pi</math> unnecessary.

;All chemistry equations
Randall implies that all chemistry is just combustion of chemicals, demonstrated with an incorrect form of a common example chemistry equation of burning Methane and Oxygen (with added heat), to form water and carbon dioxide. However, in this form "HEAT" is an actual molecule, rather than simply indicating the presence of heat to start the reaction. Thus the equation is modified to incorporate the fictional "HEAT" into the reaction. While the H in "HEAT" is the chemical symbol of the element hydrogen, none of the letters E, A, or T are symbols of any actual elements. Also, to account for the second hydrogen in "H(2)EAT" on the products side, the oxygen gas on the reactants side has been altered to be hydroxide, a strong base that would not facilitate traditional combustion.

TODO: other simplified explanations.

===Technical Explanations===
;All kinematics equations
:<math>E = K_0t + \frac{1}{2}\rho vt^2</math>
{{w|Kinematics}} describes the motion of objects without considering mass or forces. The latter is described by {{w|Kinetics (physics)|kinetics}}. The two fields get frequently confused due to the similarity of words.

This equation here literally states: "Energy equals a constant <math>K_0</math> multiplied by time, plus half of density multiplied by speed multiplied by time squared".

The first term here is hard to interpret: it could be correct if <math>K_0</math> is a constant power applied to the system, but this symbol would more normally be used to denote an initial energy, in which case multiplying by <math>t</math> would be wrong. Alternatively, the term is similar to <math>k_B T</math> (sometimes written as ''kT''), a term that often appears in {{w|Statistical_mechanics|statistical mechanics}} equations, where ''kB'' (or ''k'') is {{w|Boltzmann_constant|the Boltzmann constant}}, and ''T'' is the {{w|Thermodynamic_temperature|absolute temperature}}. In this latter case, the term would have units of energy, consistent with the left side of the equation.

The second term looks similar to the kinetic energy term <math> \frac{1}{2}\rho v^2 </math> in [http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html the Bernoulli equation] for fluids. (More properly, this is the kinetic energy ''density'' in the fluid).

The whole equation appears to be a play on the kinematics formula: <math>s = v_0t + \frac{1}{2}\ at^2</math>, where distance travelled (''s'') by a constantly accelerating object is determined by initial velocity (''v0''), time (''t''), and acceleration (''a'')

Kinematics is often one of the first topics covered in an introductory physics course, both at the high school and freshman college levels. As such, mixing in material from more advanced topics like statistical mechanics and the Bernoulli equation, even if done correctly, would be very confusing for a typical student learning kinematics.

;All number theory equations
:<math>K_n = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
{{w|Number theory}} is a branch of mathematics primarily studying the properties of integers.

Said in English, the equation can be read: "The ''n''th K-number is equal to the sum for all ''i'' from 0 to infinity of the sum for all π from 0 to infinity of ''n'' minus π, multiplied by ''i'' plus ''e'' raised to the power of π minus infinity." (''i'' here is an iteration variable, not the imaginary number constant; ''e'' is Euler's number, approximately 2.718). A twofold misconception can be seen here. The first is the use of π as a variable instead of the circle constant (3.14...). This might be a jab at how in number theory letters and numbers are used interchangeably, but where some letters are suddenly fixed constants.

Further confusion comes from the use of unusual mathematical models. While the term <math>e^{\pi-\infty}</math> is meaningless when considered in standard ("high school") mathematics, it is valid when considered on the {{w|extended real number line}}, a concept unfamiliar to most non-mathematicians and uncommon in number theory. Naively, this would signify that (with the use of π as a variable) the exponent would range from negative infinity to zero. In fact, assuming ''e'' really does mean Euler's constant (or at least a real number strictly greater than 1) the term would be zero for every π < ∞. Ultimately, the sum diverges for every ''n''.

The close proximity of the letters i, e and π also evokes {{w|Euler's identity}} <math>e^{i\pi}+1=0</math> (also written <math>e^{i\pi}=-1</math>), without actually using it, especially since both π and i are used as variables here.

;All fluid dynamics equations
:<math>\frac{\partial}{\partial t}\nabla\cdot \rho = \frac{8}{23}
\int\!\!\!\!\!\!\!\!\!\;\;\bigcirc\!\!\!\!\!\!\!\!\!\;\;\int
\rho\,ds\,dt\cdot \rho\frac{\partial}{\partial\nabla}
</math>
{{w|Fluid dynamics}} describes the movement of non-solid material. In particular for gases, the density <math>\rho</math> is often the most interesting quantity (for liquids, this is often just constant). A unique feature of fluid-dynamic equations is the presence of {{w|Advection|advection terms}}, which take the form of often strange-looking spatial derivatives. This equation turns this up to a new level by differentiating with respect to a differential operator <math>\nabla</math>, which does not make any sense at all. Also it has a contour integral which seems reminiscent to a closed-circle process like in a piston engine, but this does not really fit in the context (differential description of a gas), and it has a pair of {{w|Magic number (programming)|unexplained numbers}} <math>8</math> and <math>23</math>, probably alluding to the {{w|Heat capacity ratio|specific heat ratio}} which is often written out as the fraction <math>\tfrac{7}{5}</math>, whereas most other physics equations [[899: Number Line|avoid including any plain numbers higher than 4]].

The title text stating that the electromagnetism equation is the same as the fluid dynamics equation, but with the arbitrary 8 and 23 replaced with the permittivity and permeability of free space is likely because electromagnetism equations often have relations to fluid dynamics, and because those two constants appear in the vast majority of electromagnetism equations.

;All quantum mechanics equations
:<math>|\psi_{x,y}\rangle = A(\psi) A(|x\rangle \otimes |y\rangle)</math>
{{w|Quantum mechanics}} is a fundamental theory in physics which describes nature at scales of atoms and below. It typically uses the {{w|Bra–ket notation|bra–ket notation}} in its formulae.

This equation takes a state psi in the dimensions of x and y and equates it to an operator A performed on psi multiplied by the same operator performed on the tensor product of x and y. Since the state psi is already the tensor product of the states x and y, this is equivalent to performing the same unknown operator twice on psi, and unless this operator is the identity or is its own inverse such as a bit-flip or Hermitian operator, this equation is therefore incorrect.

;All chemistry equations
:<math>\mathrm{CH}_4 + \mathrm{OH} + \mathrm{HEAT} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CH}_2 + \mathrm{H}_2 \mathrm{EAT}</math>
A {{w|Chemical equation|chemical equation}} represents a chemical reaction as a formula, with the reactant entities on the left-hand side, and the product entities on the right-hand side. The number of each element on the left side must match those on the right side. The energy produced or absorbed in this process is not included in that formula.

This is a modification of the combustion of methane. The correct form is often taught and a good example problem but obviously there are more chemistry problems.<math>\mathrm{HEAT}</math> is normally shorthand for {{w|activation energy}}, but in Randall's version it's jokingly used as a chemical ingredient and becomes <math>\mathrm{H}_2\mathrm{EAT}</math>, taking the hydrogen atom freed by the combustion equation shown. The proper methane combustion equation would be: <math>\mathrm{CH}_4 + 2 \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2</math>

While <math>\mathrm{OH}</math> often appears in chemical equations in the form of a negatively charged hydroxide group (<math>\mathrm{OH}^-</math>), the left side of the equation involves a bare <math>\mathrm{OH}</math>, possibly the highly unstable hydroxyl radical (although this would typically be written with a leading dot, e.g. <math>\bullet\mathrm{OH}</math>). Similarly, the right side contains an unstable methylene radical which would generally only appear as an intermediate rather than a product.

;All quantum gravity equations
:<math>\mathrm{SU}(2)\mathrm{U}(1) \times \mathrm{SU}(\mathrm{U}(2))</math>
This is more similar to expressions which appear in {{w|Grand_Unified_Theory|Grand Unified Theory}} (GUT) than general quantum gravity. Unlike some of the other equations, this one has no interpretation which could make it mathematically correct. This is similar to the notations used to describe the symmetry group of a particular phenomena in terms of mathematical {{w|Lie_Group|Lie Groups}}. A real example would be the Standard Model of particle physics which has symmetry according to <math>\rm{SU(3)\times SU(2) \times U(1)}</math>. Here, <math>\rm{SU}</math> and <math>\rm{U}</math> denote the special unitary and unitary groups respectively with the numbers indicating the dimension of the group. Loosely, the three terms correspond to the symmetries of the strong force, weak force and electromagnetism although the exact correspondence is muddied by symmetry breaking and the Higgs mechanism.

Of course, an expression missing an "=" sign, is difficult to interpret as an "equation", because equations normally express an "equality" of some kind. Nobody knows whether Randal refers to a horse, zebra, donkey or other equine here.

Randall's version clearly involves some similar groups although without the <math>\times</math> symbol it is hard to work out what might be happening. A term like <math>\rm{SU(U(2))}</math> has no current interpretation in mathematics, if anyone thinks otherwise and possibly has a solution to the quantum gravity problem they should probably get in touch with someone about that.

;All gauge theory equations
:[[File:All gauge theory equations.png]]
In physics, a {{w|Gauge theory|gauge theory}} is a type of field theory which is invariant to local transformations. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom.

This equation looks broadly similar to the sorts of things which appear in gauge theory such as the equations which define {{w|Yang–Mills_theory#Quantization|Yang-Mills Theory}}. By the time physics has got this far in, people have normally run out of regular symbols making a lot of the equations look very daunting. The actual equations in this field rarely go far beyond the Greek alphabet though and no-one has yet to try putting hats on brackets. The appearance of many sub- and superscripts is normal (this links to the group theory origins of these equations) and for the layperson it can be impossible to determine which additions are labels on the symbols and which are indices for an {{w|Einstein_notation|Einstein Sum}}.

The left-hand side <math>S_g</math> is the symbol for some {{w|Action_(physics)|action}}, in Yang-Mills theory this is actually used for a so-called "ghost action". On the right-hand side we have a large number of terms, most of which are hard to interpret without knowing Randall's thought processes (this is why real research papers should all label their equations thoroughly). The <math>\frac{1}{2\bar{\varepsilon}}</math> looks like a constant of proportionality which often appears in gauge theories. The factor of <math>i = \sqrt{-1}</math> is not unusual as many of these equations use complex numbers. The <math>\eth</math> symbol looks similar to a <math>\partial</math> partial derivative symbol especially as the {{w|Dirac_equation#Covariant_form_and_relativistic_invariance|Dirac Equation}} uses a slashed version as a convenient shorthand.

The rest of the equation cannot be mathematically correct as the choice of indices used does not match that on the left-hand side (which has none). In particle physics subscripts (or superscripts) of greek letters (usually <math>\mu</math> or <math>\nu</math>) indicate terms which transform nicely under Lorentz transformations (special relativity). Roman indices from the beginning of the alphabet relate to various gauge transformation propetries, the triple index seen on <math>p^{abc}_v</math> would likely come from some <math>\rm{SU(3)}</math> transformation (related to the strong nuclear force). Since <math>S_g</math> has none of these (and is thus a scalar which remains constant under these operations), we would need the right-hand side to behave in the same way. Most of the indices which appear are unpaired and so will not result in a scalar making the equation very wrong. For those not familiar with this type of equation, this is similar to the mistake of messing up units, for instance setting a distance equal to a mass.

;All cosmology equations
:<math>H(t) + \Omega + G \cdot \Lambda \, \dots \begin{cases} \dots > 0 & \text{(Hubble model)} \\ \dots = 0 & \text{(Flat sphere model)} \\ \dots < 0 & \text{(Bright dark matter model)} \end{cases}
</math>
This is a parody of equations defining the {{w|Hubble's_law#Derivation_of_the_Hubble_parameter|Hubble Parameter}} <math>H(t)</math> although it looks like Randall has become bored and not bothered to finish his equation. Such equations usually have several <math>\Omega</math> terms representing the contributions of different substances to the energy-density of the Universe (matter, radiation, dark energy etc.). In this context <math>G</math> could be Newton's constant and <math>\Lambda</math> is the cosmological constant (energy density of empty space) although seeing them appear multiplied and on the same footing as <math>H</math> is unusual (the dot is entirely unnecessary). Choosing to make <math>H</math> a function of time <math>t</math> and not of redshift <math>z</math> is also unusual.

The second section looks like the inequalities used to show how the equation varies with the shape of the Universe, based on the value of the curvature parameter <math>\Omega_k</math>. A value of 0 indicates a flat Universe (this is more or less what we observe) while a positive /negative value indicates an open /closed curved Universe. Randall's choice of labels further makes fun of the field as both a flat sphere and bright dark matter are oxymoronic terms which would involve some rather strange model universes.

;All truly deep physics equations
:[[File:All truly deep physics equations.png]]
<math>\hat H</math> is the Hamiltonian operator, which when applied to a system returns the total energy. In this context, U would usually be the potential energy. However, there is also a subscript 0 and a diacritic marking indicating some other variable. Much of physics is based on Lagrangian and Hamiltonian mechanics. The Lagrangian is defined as <math>\hat L = \hat K - \hat U </math> with K being the kinetic energy and U the potential. Hamiltonian mechanics uses the equation <math>\hat H = \hat K + \hat U </math>. The Hamiltonian must be conserved so taking the time derivative and setting it equal to zero is a powerful tool. The "principle of least action" allows most modern physics to be derived by setting the time derivative of the Lagrangian to zero.

==Transcript==
:[Nine equations are listed, three in the top row and two in each of the next three rows. Below each equation there are labels:]

:E = K0t + 1/2 ρvt2
:All kinematics equations

:Kn = ∑i=0∞∑π=0∞(n-π)(i-eπ-∞)
:All number theory equations

:∂/∂t ∇ ⋅ ρ = 8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
:All fluid dynamics equations

:|ψx,y〉 = A(ψ) A(|x〉⊗ |y〉)
:All quantum mechanics equations

:CH4 + OH + HEAT → H2O + CH2 + H2EAT
:All chemistry equations

:SU(2)U(1) × SU(U(2))
:All quantum gravity equations

:Sg = (-1)/(2ε̄) i ð (̂ ξ0 +̊ pε ρvabc η0 )̂ f̵a0 λ(ʒ̆) ψ(0a)
:All gauge theory equations

:[There is a brace linking the three cases together.]
:H(t) + Ω + G⋅Λ ...
:... > 0 (Hubble model)
:... = 0 (Flat sphere model)
:... < 0 (Bright dark matter model)
:All cosmology equations

:Ĥ - u̧0 = 0
:All truly deep physics equations

{{comic discussion}}

[[Category:Science]]
[[Category:Physics]]
[[Category:Math]]
[[Category:Chemistry]]
[[Category:Astronomy]]

2034: Equations

2018-11-06T03:50:33Z

Adam1729: e^(pi-infty) is 0, not undefined

{{comic
| number = 2034
| date = August 17, 2018
| title = Equations
| image = equations.png
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
}}
==Explanation==
{{incomplete|TODO: some simplified explanations. Do NOT delete this tag too soon.}}

This comic gives a set of equations supposedly from different areas of science in mathematics, physics, and chemistry. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. To someone who knows even a little about the topic, they are clearly very wrong and only seem even worse the more you look at them. In many disciplines, the mathematical description of a large area is summed up in a small number of equations, such as Maxwell's equations for electromagnetism. In similar fashion, the equations here purport to encompass the whole of their given field.

===Simplified Explanations===

;All kinematics equations
Kinematics is the study of the motion of objects. More specifically, it describes how the location, velocity, and acceleration of an object vary over time. The equation shown contains two of these standard kinematic variables, velocity ''v'' and time ''t'', in addition to several quantities (''E'', ''K0'', and ''ρ'') that are completely unrelated to kinematics.

;All number theory equations
Number theory is a branch of mathematics concerned primarily with the study of integers. However, the equation shown contains the non-integer Euler's constant ''e'' (approximately 2.718). It also uses the Greek letter π as an integer-valued variable, even though the symbol π is used in mathematics almost exclusively to denote the well-known ''non''-integer circle constant (approximately 3.14159). Even with π treated as a variable here, one of its uses in the equation is still unusual, to say the least. <math>\pi-\infty</math> is just <math>-\infty</math>, so <math>e^{\pi-\infty}</math> is just 0, making the <math>\pi</math> unnecessary.

;All chemistry equations
Randall implies that all chemistry is just combustion of chemicals, demonstrated with an incorrect form of a common example chemistry equation of burning Methane and Oxygen (with added heat), to form water and carbon dioxide. However, in this form "HEAT" is an actual molecule, rather than simply indicating the presence of heat to start the reaction. Thus the equation is modified to incorporate the fictional "HEAT" into the reaction. While the H in "HEAT" is the chemical symbol of the element hydrogen, none of the letters E, A, or T are symbols of any actual elements. Also, to account for the second hydrogen in "H(2)EAT" on the products side, the oxygen gas on the reactants side has been altered to be hydroxide, a strong base that would not facilitate traditional combustion.

TODO: other simplified explanations.

===Technical Explanations===
;All kinematics equations
:<math>E = K_0t + \frac{1}{2}\rho vt^2</math>
{{w|Kinematics}} describes the motion of objects without considering mass or forces. The latter is described by {{w|Kinetics (physics)|kinetics}}. The two fields get frequently confused due to the similarity of words.

This equation here literally states: "Energy equals a constant <math>K_0</math> multiplied by time, plus half of density multiplied by speed multiplied by time squared".

The first term here is hard to interpret: it could be correct if <math>K_0</math> is a constant power applied to the system, but this symbol would more normally be used to denote an initial energy, in which case multiplying by <math>t</math> would be wrong. Alternatively, the term is similar to <math>k_B T</math> (sometimes written as ''kT''), a term that often appears in {{w|Statistical_mechanics|statistical mechanics}} equations, where ''kB'' (or ''k'') is {{w|Boltzmann_constant|the Boltzmann constant}}, and ''T'' is the {{w|Thermodynamic_temperature|absolute temperature}}. In this latter case, the term would have units of energy, consistent with the left side of the equation.

The second term looks similar to the kinetic energy term <math> \frac{1}{2}\rho v^2 </math> in [http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html the Bernoulli equation] for fluids. (More properly, this is the kinetic energy ''density'' in the fluid).

The whole equation appears to be a play on the kinematics formula: <math>s = v_0t + \frac{1}{2}\ at^2</math>, where distance travelled (''s'') by a constantly accelerating object is determined by initial velocity (''v0''), time (''t''), and acceleration (''a'')

Kinematics is often one of the first topics covered in an introductory physics course, both at the high school and freshman college levels. As such, mixing in material from more advanced topics like statistical mechanics and the Bernoulli equation, even if done correctly, would be very confusing for a typical student learning kinematics.

;All number theory equations
:<math>K_n = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
{{w|Number theory}} is a branch of mathematics primarily studying the properties of integers.

Said in English, the equation can be read: "The ''n''th K-number is equal to the sum for all ''i'' from 0 to infinity of the sum for all π from 0 to infinity of ''n'' minus π, multiplied by ''i'' plus ''e'' raised to the power of π minus infinity." (''i'' here is an iteration variable, not the imaginary number constant; ''e'' is Euler's number, approximately 2.718). A twofold misconception can be seen here. The first is the use of π as a variable instead of the circle constant (3.14...). This might be a jab at how in number theory letters and numbers are used interchangeably, but where some letters are suddenly fixed constants.

Further confusion comes from the use of unusual mathematical models. While the term <math>e^{\pi-\infty}</math> is meaningless when considered in standard ("high school") mathematics, it is valid when considered on the {{w|extended real number line}}, a concept unfamiliar to most non-mathematicians and uncommon in number theory. Naively, this would signify that (with the use of π as a variable) the exponent would range from negative infinity to zero. In fact, assuming ''e'' really does mean Euler's constant (or at least a real number strictly greater than 1) the term would be zero for every π < ∞. Ultimately, the sum diverges for every ''n''.

The close proximity of the letters i, e and π also evokes {{w|Euler's identity}} <math>e^{i\pi}+1=0</math> (also written <math>e^{i\pi}=-1</math>), without actually using it, especially since both π and i are used as variables here.

;All fluid dynamics equations
:<math>\frac{\partial}{\partial t}\nabla\cdot \rho = \frac{8}{23}
\int\!\!\!\!\!\!\!\!\!\;\;\bigcirc\!\!\!\!\!\!\!\!\!\;\;\int
\rho\,ds\,dt\cdot \rho\frac{\partial}{\partial\nabla}
</math>
{{w|Fluid dynamics}} describes the movement of non-solid material. In particular for gases, the density <math>\rho</math> is often the most interesting quantity (for liquids, this is often just constant). A unique feature of fluid-dynamic equations is the presence of {{w|Advection|advection terms}}, which take the form of often strange-looking spatial derivatives. This equation turns this up to a new level by differentiating with respect to a differential operator <math>\nabla</math>, which does not make any sense at all. Also it has a contour integral which seems reminiscent to a closed-circle process like in a piston engine, but this does not really fit in the context (differential description of a gas), and it has a pair of {{w|Magic number (programming)|unexplained numbers}} <math>8</math> and <math>23</math>, probably alluding to the {{w|Heat capacity ratio|specific heat ratio}} which is often written out as the fraction <math>\tfrac{7}{5}</math>, whereas most other physics equations [[899: Number Line|avoid including any plain numbers higher than 4]].

The title text stating that the electromagnetism equation is the same as the fluid dynamics equation, but with the arbitrary 8 and 23 replaced with the permittivity and permeability of free space is likely because electromagnetism equations often have relations to fluid dynamics, and because those two constants appear in the vast majority of electromagnetism equations.

;All quantum mechanics equations
:<math>|\psi_{x,y}\rangle = A(\psi) A(|x\rangle \otimes |y\rangle)</math>
{{w|Quantum mechanics}} is a fundamental theory in physics which describes nature at scales of atoms and below. It typically uses the {{w|Bra–ket notation|bra–ket notation}} in its formulae.

This equation takes a state psi in the dimensions of x and y and equates it to an operator A performed on psi multiplied by the same operator performed on the tensor product of x and y. Since the state psi is already the tensor product of the states x and y, this is equivalent to performing the same unknown operator twice on psi, and unless this operator is the identity or is its own inverse such as a bit-flip or Hermitian operator, this equation is therefore incorrect.

;All chemistry equations
:<math>\mathrm{CH}_4 + \mathrm{OH} + \mathrm{HEAT} \rightarrow \mathrm{H}_2\mathrm{O} + \mathrm{CH}_2 + \mathrm{H}_2 \mathrm{EAT}</math>
A {{w|Chemical equation|chemical equation}} represents a chemical reaction as a formula, with the reactant entities on the left-hand side, and the product entities on the right-hand side. The number of each element on the left side must match those on the right side. The energy produced or absorbed in this process is not included in that formula.

This is a modification of the combustion of methane. The correct form is often taught and a good example problem but obviously there are more chemistry problems.<math>\mathrm{HEAT}</math> is normally shorthand for {{w|activation energy}}, but in Randall's version it's jokingly used as a chemical ingredient and becomes <math>\mathrm{H}_2\mathrm{EAT}</math>, taking the hydrogen atom freed by the combustion equation shown. The proper methane combustion equation would be: <math>\mathrm{CH}_4 + 2 \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2\mathrm{O} + \mathrm{CO}_2</math>

While <math>\mathrm{OH}</math> often appears in chemical equations in the form of a negatively charged hydroxide group (<math>\mathrm{OH}^-</math>), the left side of the equation involves a bare <math>\mathrm{OH}</math>, possibly the highly unstable hydroxyl radical (although this would typically be written with a leading dot, e.g. <math>\bullet\mathrm{OH}</math>). Similarly, the right side contains an unstable methylene radical which would generally only appear as an intermediate rather than a product.

;All quantum gravity equations
:<math>\mathrm{SU}(2)\mathrm{U}(1) \times \mathrm{SU}(\mathrm{U}(2))</math>
This is more similar to expressions which appear in {{w|Grand_Unified_Theory|Grand Unified Theory}} (GUT) than general quantum gravity. Unlike some of the other equations, this one has no interpretation which could make it mathematically correct. This is similar to the notations used to describe the symmetry group of a particular phenomena in terms of mathematical {{w|Lie_Group|Lie Groups}}. A real example would be the Standard Model of particle physics which has symmetry according to <math>\rm{SU(3)\times SU(2) \times U(1)}</math>. Here, <math>\rm{SU}</math> and <math>\rm{U}</math> denote the special unitary and unitary groups respectively with the numbers indicating the dimension of the group. Loosely, the three terms correspond to the symmetries of the strong force, weak force and electromagnetism although the exact correspondence is muddied by symmetry breaking and the Higgs mechanism.

Of course, an expression missing an "=" sign, is difficult to interpret as an "equation", because equations normally express an "equality" of some kind. Nobody knows whether Randal refers to a horse, zebra, donkey or other equine here.

Randall's version clearly involves some similar groups although without the <math>\times</math> symbol it is hard to work out what might be happening. A term like <math>\rm{SU(U(2))}</math> has no current interpretation in mathematics, if anyone thinks otherwise and possibly has a solution to the quantum gravity problem they should probably get in touch with someone about that.

;All gauge theory equations
:[[File:All gauge theory equations.png]]
In physics, a {{w|Gauge theory|gauge theory}} is a type of field theory which is invariant to local transformations. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom.

This equation looks broadly similar to the sorts of things which appear in gauge theory such as the equations which define {{w|Yang–Mills_theory#Quantization|Yang-Mills Theory}}. By the time physics has got this far in, people have normally run out of regular symbols making a lot of the equations look very daunting. The actual equations in this field rarely go far beyond the Greek alphabet though and no-one has yet to try putting hats on brackets. The appearance of many sub- and superscripts is normal (this links to the group theory origins of these equations) and for the layperson it can be impossible to determine which additions are labels on the symbols and which are indices for an {{w|Einstein_notation|Einstein Sum}}.

The left-hand side <math>S_g</math> is the symbol for some {{w|Action_(physics)|action}}, in Yang-Mills theory this is actually used for a so-called "ghost action". On the right-hand side we have a large number of terms, most of which are hard to interpret without knowing Randall's thought processes (this is why real research papers should all label their equations thoroughly). The <math>\frac{1}{2\bar{\varepsilon}}</math> looks like a constant of proportionality which often appears in gauge theories. The factor of <math>i = \sqrt{-1}</math> is not unusual as many of these equations use complex numbers. The <math>\eth</math> symbol looks similar to a <math>\partial</math> partial derivative symbol especially as the {{w|Dirac_equation#Covariant_form_and_relativistic_invariance|Dirac Equation}} uses a slashed version as a convenient shorthand.

The rest of the equation cannot be mathematically correct as the choice of indices used does not match that on the left-hand side (which has none). In particle physics subscripts (or superscripts) of greek letters (usually <math>\mu</math> or <math>\nu</math>) indicate terms which transform nicely under Lorentz transformations (special relativity). Roman indices from the beginning of the alphabet relate to various gauge transformation propetries, the triple index seen on <math>p^{abc}_v</math> would likely come from some <math>\rm{SU(3)}</math> transformation (related to the strong nuclear force). Since <math>S_g</math> has none of these (and is thus a scalar which remains constant under these operations), we would need the right-hand side to behave in the same way. Most of the indices which appear are unpaired and so will not result in a scalar making the equation very wrong. For those not familiar with this type of equation, this is similar to the mistake of messing up units, for instance setting a distance equal to a mass.

;All cosmology equations
:<math>H(t) + \Omega + G \cdot \Lambda \, \dots \begin{cases} \dots > 0 & \text{(Hubble model)} \\ \dots = 0 & \text{(Flat sphere model)} \\ \dots < 0 & \text{(Bright dark matter model)} \end{cases}
</math>
This is a parody of equations defining the {{w|Hubble's_law#Derivation_of_the_Hubble_parameter|Hubble Parameter}} <math>H(t)</math> although it looks like Randall has become bored and not bothered to finish his equation. Such equations usually have several <math>\Omega</math> terms representing the contributions of different substances to the energy-density of the Universe (matter, radiation, dark energy etc.). In this context <math>G</math> could be Newton's constant and <math>\Lambda</math> is the cosmological constant (energy density of empty space) although seeing them appear multiplied and on the same footing as <math>H</math> is unusual (the dot is entirely unnecessary). Choosing to make <math>H</math> a function of time <math>t</math> and not of redshift <math>z</math> is also unusual.

The second section looks like the inequalities used to show how the equation varies with the shape of the Universe, based on the value of the curvature parameter <math>\Omega_k</math>. A value of 0 indicates a flat Universe (this is more or less what we observe) while a positive /negative value indicates an open /closed curved Universe. Randall's choice of labels further makes fun of the field as both a flat sphere and bright dark matter are oxymoronic terms which would involve some rather strange model universes.

;All truly deep physics equations
:[[File:All truly deep physics equations.png]]
<math>\hat H</math> is the Hamiltonian operator, which when applied to a system returns the total energy. In this context, U would usually be the potential energy. However, there is also a subscript 0 and a diacritic marking indicating some other variable. Much of physics is based on Lagrangian and Hamiltonian mechanics. The Lagrangian is defined as <math>\hat L = \hat K - \hat U </math> with K being the kinetic energy and U the potential. Hamiltonian mechanics uses the equation <math>\hat H = \hat K + \hat U </math>. The Hamiltonian must be conserved so taking the time derivative and setting it equal to zero is a powerful tool. The "principle of least action" allows most modern physics to be derived by setting the time derivative of the Lagrangian to zero.

==Transcript==
:[Nine equations are listed, three in the top row and two in each of the next three rows. Below each equation there are labels:]

:E = K0t + 1/2 ρvt2
:All kinematics equations

:Kn = ∑i=0∞∑π=0∞(n-π)(i-eπ-∞)
:All number theory equations

:∂/∂t ∇ ⋅ ρ = 8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
:All fluid dynamics equations

:|ψx,y〉 = A(ψ) A(|x〉⊗ |y〉)
:All quantum mechanics equations

:CH4 + OH + HEAT → H2O + CH2 + H2EAT
:All chemistry equations

:SU(2)U(1) × SU(U(2))
:All quantum gravity equations

:Sg = (-1)/(2ε̄) i ð (̂ ξ0 +̊ pε ρvabc η0 )̂ f̵a0 λ(ʒ̆) ψ(0a)
:All gauge theory equations

:[There is a brace linking the three cases together.]
:H(t) + Ω + G⋅Λ ...
:... > 0 (Hubble model)
:... = 0 (Flat sphere model)
:... < 0 (Bright dark matter model)
:All cosmology equations

:Ĥ - u̧0 = 0
:All truly deep physics equations

{{comic discussion}}

[[Category:Science]]
[[Category:Physics]]
[[Category:Math]]
[[Category:Chemistry]]
[[Category:Astronomy]]

1878: Earth Orbital Diagram

2017-08-20T23:13:33Z

Adam1729: /* Explanation */

{{comic
| number = 1878
| date = August 18, 2017
| title = Earth Orbital Diagram
| image = earth_orbital_diagram.png
| titletext = You shouldn't look directly at a partial eclipse because of the damage that can be caused by improperly aligning the solar-lunar orbital plane with the orbital bones around your eye.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic is the third consecutive comic published in the week before the {{w|solar eclipse}} occurring on Monday, {{w|Solar eclipse of August 21, 2017|August 21, 2017}} which is a total solar eclipse and visible in totality within a band across the {{w|contiguous United States}} from west to east. The other comics are [[1876: Eclipse Searches]] and [[1877: Eclipse Science]].

The comic claims that the reason that eclipses don't happen every month is simple to understand by looking at an orbital diagram. Ironically, the cartoon has so many parts and labels that it is far more difficult to understand than is implied. While the graph itself is based on {{w|Orbital elements|astronomical definitions}}, all the labels are nonsense in this context. In effect, the comic is a parody of a common joke in which a person asks a scientist a question, the scientist begins by saying "It's really quite simple", then proceeds to give a very lengthy and highly technical explanation that non-scientists would not be expected to understand.

All of the labels in the diagram are complicated words or phrases. Some are related to orbital mechanics (e.g. "equinox" and "perihelion"), while others are wholly unrelated or even made up. Each label is nonsensical in its place in the diagram. Compare/contrast with the standard {{w|Kepler orbit|Kepler Orbit}} diagram.

The title text references warnings to not look directly into the sun, but parodies those warnings by referring to 'orbit', the anatomical term for the eye socket.

===Labels and Their Astronomical Meanings===

;Arctangent
*{{w|Arctangent}} is the inverse function of the tangent function of trigonometry. You can determine a non-right angle of a right triangle by taking the arctangent of the length of the opposite side divided by the length of the adjacent side.
*The angle shown in the comic has no astronomical meaning.

;Astral plane
*The {{w|Astral plane}} is a plane of existence in various esoteric theories. It features prominently in Dungeons and Dragons cosmology, connecting the various other planes of existence.
*The picture shows the {{w|Orbit_of_the_Moon|lunar orbital plane}}, the plane in which the Moon orbits the Earth, tilted about 5.1 degrees from the ecliptic.

;Declension
*{{w|Declension}} is the inflection of nouns in a language. In this comic, it might be a portmanteau of declination and (right) ascension.
*In astronomy, the {{w|Declination|declination}} is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system. It is measured north or south of the celestial equator, like the geographical latitude on Earth. But in the picture the label is at the angle for the axial tilt of the Earth.
*And the {{w|Right_ascension|right ascension}} is the angular distance measured eastward along the celestial equator from the vernal equinox to the hour circle of the point in question.

;Determinant of the date of Easter
*In Western Christianity {{w|Easter}} always falls on the first Sunday after the first ecclesiastical full moon after the beginning of spring (equinox). The ecclesiastical full moon is determined by a calendar that approximates the actual time of the full moon, Thus the date of easter is defined by a combination of a solar and a moon calendar. The position of that angle isn't that bad but it should be not more than 30 degrees (slightly more than one month.)
*In mathematics, the determinant is a function of numerical matrices. In this context, however, it apparently refers to something that directly determines the date of Easter.

;Dimples of Venus
*The {{w|Dimples of Venus}} are indentations sometimes visible on the human lower back.
*In astronomy the {{w|Belt of Venus}} is a shadow cast by the Earth visible in its atmosphere.

;Enceliopsis
*{{w|Enceliopsis}} are small genus of flowering plants in the daisy family, appropriately known as "sunrays".
*In astronomy this point has also no specific meaning. But {{w|Enceladus}} is a moon around {{w|Saturn}}.

;Equinox / Solstice
{{w|Equinox}} and {{w|Solstice}} have very different meanings:
*An Equinox is one of two instants in the year when the sun is exactly over the equator; the length of day and night are very nearly equal that day at all locations on the planet, and (in the United States) it is the first day of Spring or Autumn, depending on the time of year.
*A Solstice is one of two instants in the year when the sun's angle is maximally far from Earth's equator; when one occurs, the length of the day or night is shortest or longest (depending on whether one is in the northern or southern hemisphere), and (in the United States) it marks the first day of summer or winter.

Both types occur because the Earth's rotation axis is tilted (at 23.4 degrees) from its orbital plane (ecliptic) about the Sun.

Jokingly insisting that two different terms are American/British variants of the same word has been the topic of [[1677: Contrails]].

;Hypothecate
*{{w|Hypothecate}} is a legal verb that means something similar to "make a mortgage".
*The {{w|hypotenuse}} is the longest side of a right-angled triangle. Here it is an unrelated length, approximately equal to the diameter of the sun (half the angular size of the sun times twice the distance to it).

;Obsequity
*Obsequity means the state of being obsequious (showing an indecorous willingness to obey or serve, or "sucking up").
*In astronomy the correct word is {{w|Obliquity}}, meaning an axial tilt.

;Perihelix
*This is a portmanteau of helix and perihelion.
*The {{w|perihelion}} is the point in a elliptical solar orbit that is closest to the Sun.

;Prolapse
*A {{w|Prolapse}} is a medical condition in which an internal organ is slipped forward or down.
*{{w|Retrograde and prograde motion}} are terms used to describe the apparent motion of celestial objects through the sky.

;Sagittal plane
*The {{w|Sagittal plane}} is an anatomical plane, dividing the body in left and right.
*The correct label in the picture would be the {{w|Ecliptic plane}}. The plane the Earth orbits the Sun.
*{{w|Sagittarius (constellation)|Sagittarius}} is one of the stellar constellations of the Zodiac. The center of the Milky Way lies in this constellation.

;Solar plexus
*The {{w|Solar plexus}} is a network of nerves located in the abdomen. It was the name of [[64: Solar Plexus]].
*{{w|Solar}} is an adjective referring to the Sun, the star in our solar system.

;Tropopause
*The {{w|Tropopause}} is the boundary in our atmosphere between the troposphere and stratosphere, defined as the boundary where air ceases to cool with increasing elevation. It is 9-17 km above sea level, not the thousands of kilometers as depicted here.
*The label appears to point at the orbit of the moon.

;Angle between the Astral and the Sagittal Planes
* The angle depicted is the inclination of the moon orbit. The planes are marked with the symbol for the Capricorn zodiac sign and an unknown symbol respectively; the angle is marked with the greek letter ''phi'' (ϕ), except with two vertical lines (as if it was a currency unit, similarly to the euro sign).

;Errata
* Errata are corrections in a published text (e.g. a newspaper article) issued after the publication.
* The angle depicted as errata is half the angular size of the sun, which has to match the lunar angular size to cause a solar total eclipse.

==Explanation for "Why isn't there a (solar) eclipse every month?"==

If the plane of where the Earth orbits the Sun and where the Moon orbits the Earth were completely aligned, then there would be a solar eclipse at every new moon (once every {{w|Orbit_of_the_Moon#Lunar_periods| 29.5 days}}) and a lunar eclipse at every full moon (half a lunar period about 14.7 days after a New Moon). However, the plane in which the Moon orbits the Earth is tilted with an inclination of 5 degrees relative to that of the ecliptic plane (the plane defined by the Earth's orbit around the Sun). Eclipses are only possible during two eclipse seasons each year (half a year apart) where for a period of 31 to 37 days the Sun is nearly aligned with the two points in the tilted Earth-Moon plane where the Moon crosses the ecliptic plane. During an eclipse season at the time of a new moon there will be solar eclipses visible from certain locations and during full moons there will be lunar eclipses.

[[Image:Eclipse_Diagram.jpg]]

The real explanation of eclipses is evident from this xkcd comic, but is labeled with a fictional character similar to a Greek phi but with two vertical lines; the remaining labels also do not contribute to this explanation and exist only to distract or misinform the reader.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[An orbital map of the Earth is shown. The Sun is in the center, the Earth is at the right bottom, and the Moon is left below the Earth.]
:'''Why isn't there an eclipse every month?'''
:This is a common question! The answer is made clear by a quick look at the Earth's orbital diagram:

:[Label Sun:]
:Solar plexus

:[Label on the Earth's plane:]
:Sagittal plane

:[Labels on Earth's orbit (beginning at the Earth counterclockwise):]
:Perihelix, Declension, Obsequity, Hypothecate, Enceliopsis, Equinox (''Solstice'' in British English)

:[Two angles in the plane are labeled as:]
:Determinant of the date of Easter, Arctangent

:[The plane of the Moon is pictured in a small angle to the Earth's plane and named Astral Plane. The angle is presented between two lines (Greek Nu or Gamma and a double Greek Chi) and identified by a "Game Of Thrones" 'O' (a character that looks similar to a Greek Phi but with two vertical lines).]
:[The labels at the Moon's path are:]
:Tropopause, Prolapse, Errata.

:[An arrow points to the Earth at the zero meridian on the equator. The label reads:]
:Dimples of Venus

{{comic discussion}}

[[Category:Astronomy]]

1878: Earth Orbital Diagram

2017-08-20T23:07:46Z

Adam1729: /* Explanation */

{{comic
| number = 1878
| date = August 18, 2017
| title = Earth Orbital Diagram
| image = earth_orbital_diagram.png
| titletext = You shouldn't look directly at a partial eclipse because of the damage that can be caused by improperly aligning the solar-lunar orbital plane with the orbital bones around your eye.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic is the third consecutive comic published in the week before the {{w|solar eclipse}} occurring on Monday, {{w|Solar eclipse of August 21, 2017|August 21, 2017}} which is a total solar eclipse and visible in totality within a band across the {{w|contiguous United States}} from west to east. The other comics are [[1876: Eclipse Searches]] and [[1877: Eclipse Science]].

The comic claims that the reason that eclipses don't happen every month is simple to understand by looking at an orbital diagram. Ironically, the cartoon has so many parts and labels that it is far more difficult to understand than is implied. While the graph itself is based on {{w|Orbital elements|astronomical definitions}}, all the labels are nonsense in this context. In effect, the comic is a parody of a common joke in which a person asks a scientist a question, the scientist begins by saying "It's really quite simple", then proceeds to give a very lengthy and highly technical explanation that non-scientists would not be expected to understand.

All of the labels in the diagram are complicated words or phrases. Some are related to orbital mechanics (e.g. "equinox" and "perihelion"), while others are wholly unrelated or even made up. Each label is nonsensical in its place in the diagram. Compare/contrast with the standard {{w|Kepler orbit|Kepler Orbit}} diagram.

The title text references warnings to not look directly into the sun, but parodies those warnings by referring to 'orbit', the anatomical term for the eye socket.

===Labels and Their Astronomical Meanings===

;Arctangent
*{{w|Arctangent}} is the inverse function of the tangent function of trigonometry. You can determine a non-right angle of a right triangle by taking the arctangent of the length of the opposite side divided by the length of the adjacent side.
*The angle shown in the comic has no astronomical meaning.

;Astral plane
*The {{w|Astral plane}} is a plane of existence in various esoteric theories. It features prominently in Dungeons and Dragons cosmology, connecting the various other planes of existence.
*The picture shows the {{w|Orbit_of_the_Moon|lunar orbital plane}}, the plane in which the Moon orbits the Earth, tilted about 5.1 degrees from the ecliptic.

;Declension
*{{w|Declension}} is the inflection of nouns in a language.
*In astronomy, the {{w|Declination|declination}} is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system. It is measured north or south of the celestial equator, like the geographical latitude on Earth. But in the picture the label is at the angle for the axial tilt of the Earth.

;Determinant of the date of Easter
*In Western Christianity {{w|Easter}} always falls on the first Sunday after the first ecclesiastical full moon after the beginning of spring (equinox). The ecclesiastical full moon is determined by a calendar that approximates the actual time of the full moon, Thus the date of easter is defined by a combination of a solar and a moon calendar. The position of that angle isn't that bad but it should be not more than 30 degrees (slightly more than one month.)
*In mathematics, the determinant is a function of numerical matrices. In this context, however, it apparently refers to something that directly determines the date of Easter.

;Dimples of Venus
*The {{w|Dimples of Venus}} are indentations sometimes visible on the human lower back.
*In astronomy the {{w|Belt of Venus}} is a shadow cast by the Earth visible in its atmosphere.

;Enceliopsis
*{{w|Enceliopsis}} are small genus of flowering plants in the daisy family, appropriately known as "sunrays".
*In astronomy this point has also no specific meaning. But {{w|Enceladus}} is a moon around {{w|Saturn}}.

;Equinox / Solstice
{{w|Equinox}} and {{w|Solstice}} have very different meanings:
*An Equinox is one of two instants in the year when the sun is exactly over the equator; the length of day and night are very nearly equal that day at all locations on the planet, and (in the United States) it is the first day of Spring or Autumn, depending on the time of year.
*A Solstice is one of two instants in the year when the sun's angle is maximally far from Earth's equator; when one occurs, the length of the day or night is shortest or longest (depending on whether one is in the northern or southern hemisphere), and (in the United States) it marks the first day of summer or winter.

Both types occur because the Earth's rotation axis is tilted (at 23.4 degrees) from its orbital plane (ecliptic) about the Sun.

Jokingly insisting that two different terms are American/British variants of the same word has been the topic of [[1677: Contrails]].

;Hypothecate
*{{w|Hypothecate}} is a legal verb that means something similar to "make a mortgage".
*The {{w|hypotenuse}} is the longest side of a right-angled triangle. Here it is an unrelated length, approximately equal to the diameter of the sun (half the angular size of the sun times twice the distance to it).

;Obsequity
*Obsequity means the state of being obsequious (showing an indecorous willingness to obey or serve, or "sucking up").
*In astronomy the correct word is {{w|Obliquity}}, meaning an axial tilt.

;Perihelix
*This is a portmanteau of helix and perihelion.
*The {{w|perihelion}} is the point in a elliptical solar orbit that is closest to the Sun.

;Prolapse
*A {{w|Prolapse}} is a medical condition in which an internal organ is slipped forward or down.
*{{w|Retrograde and prograde motion}} are terms used to describe the apparent motion of celestial objects through the sky.

;Sagittal plane
*The {{w|Sagittal plane}} is an anatomical plane, dividing the body in left and right.
*The correct label in the picture would be the {{w|Ecliptic plane}}. The plane the Earth orbits the Sun.
*{{w|Sagittarius (constellation)|Sagittarius}} is one of the stellar constellations of the Zodiac. The center of the Milky Way lies in this constellation.

;Solar plexus
*The {{w|Solar plexus}} is a network of nerves located in the abdomen. It was the name of [[64: Solar Plexus]].
*{{w|Solar}} is an adjective referring to the Sun, the star in our solar system.

;Tropopause
*The {{w|Tropopause}} is the boundary in our atmosphere between the troposphere and stratosphere, defined as the boundary where air ceases to cool with increasing elevation. It is 9-17 km above sea level, not the thousands of kilometers as depicted here.
*The label appears to point at the orbit of the moon.

;Angle between the Astral and the Sagittal Planes
* The angle depicted is the inclination of the moon orbit. The planes are marked with the symbol for the Capricorn zodiac sign and an unknown symbol respectively; the angle is marked with the greek letter ''phi'' (ϕ), except with two vertical lines (as if it was a currency unit, similarly to the euro sign).

;Errata
* Errata are corrections in a published text (e.g. a newspaper article) issued after the publication.
* The angle depicted as errata is half the angular size of the sun, which has to match the lunar angular size to cause a solar total eclipse.

==Explanation for "Why isn't there a (solar) eclipse every month?"==

If the plane of where the Earth orbits the Sun and where the Moon orbits the Earth were completely aligned, then there would be a solar eclipse at every new moon (once every {{w|Orbit_of_the_Moon#Lunar_periods| 29.5 days}}) and a lunar eclipse at every full moon (half a lunar period about 14.7 days after a New Moon). However, the plane in which the Moon orbits the Earth is tilted with an inclination of 5 degrees relative to that of the ecliptic plane (the plane defined by the Earth's orbit around the Sun). Eclipses are only possible during two eclipse seasons each year (half a year apart) where for a period of 31 to 37 days the Sun is nearly aligned with the two points in the tilted Earth-Moon plane where the Moon crosses the ecliptic plane. During an eclipse season at the time of a new moon there will be solar eclipses visible from certain locations and during full moons there will be lunar eclipses.

[[Image:Eclipse_Diagram.jpg]]

The real explanation of eclipses is evident from this xkcd comic, but is labeled with a fictional character similar to a Greek phi but with two vertical lines; the remaining labels also do not contribute to this explanation and exist only to distract or misinform the reader.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[An orbital map of the Earth is shown. The Sun is in the center, the Earth is at the right bottom, and the Moon is left below the Earth.]
:'''Why isn't there an eclipse every month?'''
:This is a common question! The answer is made clear by a quick look at the Earth's orbital diagram:

:[Label Sun:]
:Solar plexus

:[Label on the Earth's plane:]
:Sagittal plane

:[Labels on Earth's orbit (beginning at the Earth counterclockwise):]
:Perihelix, Declension, Obsequity, Hypothecate, Enceliopsis, Equinox (''Solstice'' in British English)

:[Two angles in the plane are labeled as:]
:Determinant of the date of Easter, Arctangent

:[The plane of the Moon is pictured in a small angle to the Earth's plane and named Astral Plane. The angle is presented between two lines (Greek Nu or Gamma and a double Greek Chi) and identified by a "Game Of Thrones" 'O' (a character that looks similar to a Greek Phi but with two vertical lines).]
:[The labels at the Moon's path are:]
:Tropopause, Prolapse, Errata.

:[An arrow points to the Earth at the zero meridian on the equator. The label reads:]
:Dimples of Venus

{{comic discussion}}

[[Category:Astronomy]]

1878: Earth Orbital Diagram

2017-08-20T18:26:41Z

Adam1729: /* Labels and Their Astronomical Meanings */

{{comic
| number = 1878
| date = August 18, 2017
| title = Earth Orbital Diagram
| image = earth_orbital_diagram.png
| titletext = You shouldn't look directly at a partial eclipse because of the damage that can be caused by improperly aligning the solar-lunar orbital plane with the orbital bones around your eye.
}}

==Explanation==
{{incomplete|Created by a BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic is the third consecutive comic published in the week before the {{w|solar eclipse}} occurring on Monday, {{w|Solar eclipse of August 21, 2017|August 21, 2017}} which is a total solar eclipse and visible in totality within a band across the {{w|contiguous United States}} from west to east. The other comics are [[1876: Eclipse Searches]] and [[1877: Eclipse Science]].

The comic claims that the reason that eclipses don't happen every month is simple to understand by looking at an orbital diagram. Ironically, the cartoon has so many parts and labels that it is far more difficult to understand than is implied. While the graph itself is based on {{w|Orbital elements|astronomical definitions}}, all the labels are nonsense in this context. In effect, the comic is a parody of a common joke in which a person asks a scientist a question, the scientist begins by saying "It's really quite simple", then proceeds to give a very lengthy and highly technical explanation that non-scientists would not be expected to understand.

All of the labels in the diagram are complicated words or phrases. Some are related to orbital mechanics (e.g. "equinox" and "perihelion"), while others are wholly unrelated or even made up. Each label is nonsensical in its place in the diagram. Compare/contrast with the standard {{w|Kepler orbit|Kepler Orbit}} diagram.

The title text references warnings to not look directly into the sun, but parodies those warnings by referring to 'orbit', the anatomical term for the eye socket.

===Labels and Their Astronomical Meanings===

;Arctangent
*{{w|Arctangent}} is the inverse function of the tangent function of trigonometry. You can determine a non-right angle of a right triangle by taking the arctangent of the length of the opposite side divided by the length of the adjacent side.
*The angle shown in the comic has no astronomical meaning.

;Astral plane
*The {{w|Astral plane}} is a plane of existence in various esoteric theories. It features prominently in Dungeons and Dragons cosmology, connecting the various other planes of existence.
*The picture shows the {{w|Orbit_of_the_Moon|lunar orbital plane}}, the plane in which the Moon orbits the Earth, tilted about 5.1 degrees from the ecliptic.

;Declension
*{{w|Declension}} is the inflection of nouns in a language.
*In astronomy, the {{w|Declination|declination}} is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system. It is measured north or south of the celestial equator, like the geographical latitude on Earth. But in the picture the label is at the angle for the axial tilt of the Earth.

;Determinant of the date of Easter
*In Western Christianity {{w|Easter}} always falls on the first Sunday after the first ecclesiastical full moon after the beginning of spring (equinox). The ecclesiastical full moon is determined by a calendar that approximates the actual time of the full moon, Thus the date of easter is defined by a combination of a solar and a moon calendar. The position of that angle isn't that bad but it should be not more than 30 degrees (slightly more than one month.)
*In mathematics, the determinant is a function of numerical matrices. In this context, however, it apparently refers to something that directly determines the date of Easter.

;Dimples of Venus
*The {{w|Dimples of Venus}} are indentations sometimes visible on the human lower back.
*In astronomy the {{w|Belt of Venus}} is a shadow cast by the Earth visible in its atmosphere.

;Enceliopsis
*{{w|Enceliopsis}} are small genus of flowering plants in the daisy family, appropriately known as "sunrays".
*In astronomy this point has also no specific meaning. But {{w|Enceladus}} is a moon around {{w|Saturn}}.

;Equinox / Solstice
{{w|Equinox}} and {{w|Solstice}} have very different meanings:
*An Equinox is one of two instants in the year when the sun is exactly over the equator; the length of day and night are very nearly equal that day at all locations on the planet, and (in the United States) it is the first day of Spring or Autumn, depending on the time of year.
*A Solstice is one of two instants in the year when the sun's angle is maximally far from Earth's equator; when one occurs, the length of the day or night is shortest or longest (depending on whether one is in the northern or southern hemisphere), and (in the United States) it marks the first day of summer or winter.

Both types occur because the Earth's rotation axis is tilted (at 23.4 degrees) from its orbital plane (ecliptic) about the Sun.

Jokingly insisting that two different terms are American/British variants of the same word has been the topic of [[1677: Contrails]].

;Hypothecate
*{{w|Hypothecate}} is a legal verb that means something similar to "make a mortgage".
*The {{w|hypotenuse}} is the longest side of a right-angled triangle. Here it is a length with no astronomical term. In terms of this comic, it's approximately the diameter of the earth's orbit times the errata.

;Obsequity
*Obsequity means the state of being obsequious (showing an indecorous willingness to obey or serve, or "sucking up").
*In astronomy the correct word is {{w|Obliquity}}, meaning an axial tilt.

;Perihelix
*This is a portmanteau of helix and perihelion.
*The {{w|perihelion}} is the point in a elliptical solar orbit that is closest to the Sun.

;Prolapse
*A {{w|Prolapse}} is a medical condition in which an internal organ is slipped forward or down.
*{{w|Retrograde and prograde motion}} are terms used to describe the apparent motion of celestial objects through the sky.

;Sagittal plane
*The {{w|Sagittal plane}} is an anatomical plane, dividing the body in left and right.
*The correct label in the picture would be the {{w|Ecliptic plane}}. The plane the Earth orbits the Sun.
*{{w|Sagittarius (constellation)|Sagittarius}} is one of the stellar constellations of the Zodiac. The center of the Milky Way lies in this constellation.

;Solar plexus
*The {{w|Solar plexus}} is a network of nerves located in the abdomen. It was the name of [[64: Solar Plexus]].
*{{w|Solar}} is an adjective referring to the Sun, the star in our solar system.

;Tropopause
*The {{w|Tropopause}} is the boundary in our atmosphere between the troposphere and stratosphere, defined as the boundary where air ceases to cool with increasing elevation. It is 9-17 km above sea level, not the thousands of kilometers as depicted here.

;Angle between the Astral and the Sagittal Planes
* The angle depicted is the inclination of the moon orbit. The planes are marked with greek letters, the angle is marked with the greek letter ''phi'' (ϕ).

;Errata
* Errata are corrections in a published text (e.g. a newspaper article) issued after the publication.
* The angle depicted as errata is half the angular size of the sun, which has to match the lunar angular size to cause a solar total eclipse.

==Explanation for "Why isn't there a (solar) eclipse every month?"==

If the plane of where the Earth orbits the Sun and where the Moon orbits the Earth were completely aligned, then there would be a solar eclipse at every new moon (once every {{w|Orbit_of_the_Moon#Lunar_periods| 29.5 days}}) and a lunar eclipse at every full moon (half a lunar period about 14.7 days after a New Moon). However, the plane in which the Moon orbits the Earth is tilted with an inclination of 5 degrees relative to that of the ecliptic plane (the plane defined by the Earth's orbit around the Sun). Eclipses are only possible during two eclipse seasons each year (half a year apart) where for a period of 31 to 37 days the Sun is nearly aligned with the two points in the tilted Earth-Moon plane where the Moon crosses the ecliptic plane. During an eclipse season at the time of a new moon there will be solar eclipses visible from certain locations and during full moons there will be lunar eclipses.

[[Image:Eclipse_Diagram.jpg]]

The real explanation of eclipses is evident from this xkcd comic, but is labeled with a fictional character similar to a Greek phi but with two vertical lines; the remaining labels also do not contribute to this explanation and exist only to distract or misinform the reader.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[An orbital map of the Earth is shown. The Sun is in the center, the Earth is at the right bottom, and the Moon is left below the Earth.]
:'''Why isn't there an eclipse every month?'''
:This is a common question! The answer is made clear by a quick look at the Earth's orbital diagram:

:[Label Sun:]
:Solar plexus

:[Label on the Earth's plane:]
:Sagittal plane

:[Labels on Earth's orbit (beginning at the Earth counterclockwise):]
:Perihelix, Declension, Obsequity, Hypothecate, Enceliopsis, Equinox (''Solstice'' in British English)

:[Two angles in the plane are labeled as:]
:Determinant of the date of Easter, Arctangent

:[The plane of the Moon is pictured in a small angle to the Earth's plane and named Astral Plane. The angle is presented between two lines (Greek Nu or Gamma and a double Greek Chi) and identified by a "Game Of Thrones" 'O' (a character that looks similar to a Greek Phi but with two vertical lines).]
:[The labels at the Moon's path are:]
:Tropopause, Prolapse, Errata.

:[An arrow points to the Earth at the zero meridian on the equator. The label reads:]
:Dimples of Venus

{{comic discussion}}

[[Category:Astronomy]]